### Woodford: Rules for Monetary Policy

This is an NBER Research Summary by Michael Woodford highlighting some of his work on monetary policy. Woodford has done a considerable amount of work on monetary policy rules, including this influential book, and this summary highlights three areas of his research (1) Inflation Stabilization and Welfare, (2) Expectations and Optimal Policy, and (3) Optimal Target Criteria for Policy.

Parts of the summary are fairly technical and I don't think the technical parts will be of general interest, and covering all three sections in a single post is too much. So I am going to focus on two important issues from part (1) that are often misunderstood. First, how is it that stabilizing inflation results in stable output growth? Why does the Fed pay so much attention to deviations of inflation from target rather than to deviations of output from target? Isn't output more important? If so, shouldn't deviations of output and employment from target be the focus of policy? Second, why do we use core inflation rather than overall inflation in the conduct of policy? Why throw out important prices such as oil and food, prices that hit a consumer's pocketbook fairly hard? Is there some theoretical justification for this? Here's Woodford:

Rules for Monetary Policy, NBER Reporter Research Summary, by Michael Woodford: ...

Inflation Stabilization and WelfareOne goal of my research has been to clarify which kinds of macroeconomic stabilization objectives best serve economic welfare. ... [I]t is not immediately obvious what the conventional goals of monetary stabilization policy --- especially the nearly universal emphasis that central banks place on maintaining a low and stable inflation rate --- have to do with consumer welfare; after all, the arguments of household utility functions generally are assumed to be the quantities of various goods and services, but not their prices. Nonetheless, I have shown that in familiar classes of sticky-price dynamic stochastic general equilibrium (DSGE) models --- models that incorporate key elements of ... empirical models of the monetary transmission mechanism... --- it is possible to show that the expected utility of the representative household varies ... with ... measures of price and wage inflation on the one hand and measures of real activity relative to a (time-varying) target level of activity on the other. Thus, it makes sense to rank alternative monetary policies according to how well they stabilize (an appropriate measure of) inflation on the one hand, and how well they stabilize (an appropriate measure of) the output gap on the other. The theory clarifies both the appropriate definition of these stabilization objectives, and the appropriate relative weights to assign to them...The answer obtained depends, of course, on the structure of the economy. In particular, inflation variability reduces welfare because of the presence of nominal rigidities; the precise nature of these rigidities determines the appropriate form of the inflation-stabilization objective. For example, if wages are flexible ..., and price adjustments are staggered in the way assumed ... by Guillermo Calvo ..., then inflation variation results in distortions caused by the misalignment of prices that are adjusted at different times. The resulting welfare losses are proportional to the ... squared deviations of the inflation rate from zero. Other assumptions about the timing of price adjustments also imply that inflation variations reduce welfare, but with a different form of loss function...

The theory also provides important insights into the question of

whichprice index or indexes it is more important to stabilize. Again, the answer depends on the nature of the nominal rigidities. If prices are adjusted more frequently in some sectors of the economy than in others, then the welfare-theoretic loss function puts more weight on variations in prices in the sectors where prices are stickier... This provides a theoretical basis for seeking to stabilize an appropriately defined measure of "core" inflation rather than an equally weighted price index. .... Similarly, if wages are sticky as are goods prices, as implied by many empirical ... models, then instability in the rate of growth of a broad index of nominal wages results in distortions similar to those created by variations in goods price inflation. If [adjustments in] wages are staggered ..., then the welfare-theoretic loss function includes a term proportional to the squared rate of goods price inflation and another term proportional to the squared rate of wage inflation each period. In this case, optimal policy involves a tradeoff between inflation stabilization, nominal wage growth stabilization, and output-gap stabilization...

Summarizing, the first issue is related to a concept known as "divine coincidence" and Mankiw has a nice discussion of this. The question is whether stabilizing inflation alone (and not worrying about output at all in the policy rule) also optimally stabilizes output. If so, then a pure inflation target is optimal, i.e. the policy rule does not contain an output term, ff = a + b(π - π*), where * means target value. In such a case, there is "divine coincidence" because stabilizing inflation coincidentally optimally stabilizes output.

It turns out that divine coincidence is a special case and that in general an output term is needed in the policy rule, i.e. ff = a + b(π - π*) + c(y - y*) as in the standard Taylor rule formulation. As Woodford discussed above, sometimes another term for wage inflation is needed in the policy rule (and there are other variations, e.g. adding an output growth term along with the level), but let's stick with the simple Taylor rule version. The point is that in general the optimal value of b will be much larger than the optimal value of c so that the monetary authority should be much more sensitive to inflation shocks than to output shocks (e.g. b=1.5 and c=.5 is common, and in many models b too small is problematic). So, even when the output gap matters, theory still says to pay the most attention to the inflation terms.

The second issue is fairly intuitive. The reason for output variation and resource misallocation in these models is the assumption of sticky prices. When prices are sticky and there is inflation, relative prices are driven away from their optimal values and this causes output to move away from its optimal value. Because of this, it is the industries with sticky prices that are most affected by inflation and suffer the largest losses (I am ignoring the indexing issue for those who may be wondering). Thus, by stabilizing these prices around their optimal values, losses are reduced. There is no need to place a large weight on flexible price industries (e.g. food and oil) because inflation does not drive those prices from their optimal values, those prices are able to respond flexibly to changing conditions.

It is not a matter of which prices appear in a consumer's bundle of goods, a point that is widely misunderstood, those will include both sticky and flexible prices. The point of policy is to stabilize the prices most likely to cause deviations from optimal values. Because of this, theory tells us the core inflation measure should place most of the weight on the fixed, not the flexible prices, and prices such as food and oil ought to be removed from the index or receive little weight. Trimming the mean, as in the popular PCE trimmed mean measures of prices and inflation used by the Fed, is intended to accomplish the task of removing the highly volatile (i.e. non-sticky) price movements.

Posted by Mark Thoma on Monday, April 3, 2006 at 12:58 AM in Academic Papers, Economics, Inflation, Monetary Policy |
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